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Rectangular Microstrip Inductor with Strip Bridge and Optional Cover (EM Quasi-Static): MRINDSBC



MRINDSBC models a microstrip rectangular inductor with strip bridge. The bridge conductor is capacitively coupled to all crossed segments. MRINDSBC differs from MRINDSB3 in that it uses substrate with optional cover MSUBC instead of MSUB. MSUBC allows to place/remove PEC cover above the inductor. As well as MRINDSN3, this model is based on an evaluation of self and mutual inductances, capacitances, and resistances between all parallel segments, which in turn is based on an accurate quasi-static model of an arbitrary number of edge-coupled microstrip lines. Similar to MRINDSB3, MRINDSBC features a switch parameter to allow an underpass bridge for GaAs designs.



Name Description Unit Type Default
ID Element ID Text MI1
NS Number of linear segments (>=4)   15
L1 Length of first segment Length 80 um
L2 Length of second segment Length 155 um
L3 Length of third segment Length 165 um
LN Length of last segment Length 35 um
AB Angle of bridge departure Angle 0 deg
W Conductor width Length 10 um
S Conductor spacing Length 5 um
WB Width of bridge strip conductor Length 10 um
HB Height of bridge dielectric Length 2 um
LB Length of bridge extension beyond inductor Length 0 um
EPSB Relative dielectric constant of bridge dielectric   1
TDB Loss tangent of bridge dielectric   0
TB Thickness of bridge strip Length 1 um
RhoB Bridge metal bulk resistivity normalized to gold   1
BrMode Switch Overpass/Underpass Text Overpass
*Acc Accuracy parameter   1
MSUBC Substrate definition Text MSUBC1[1]

[1] Modify only if schematic contains multiple substrates. See “Using Elements With Model Blocks” for details.

* indicates a secondary parameter

Parameter Details

NS. The number of linear conductor segments forming the inductor. NS should be greater than 4 and less than NSMAX. The value of NSMAX can be evaluated from the condition LNMAX >0, where

LNMAX = L2-(NS-2)(W+S)/2 for even NS

LNMAX = L3-(NS-3)(W+S)/2 for odd NS

The layout feasibility check is run before performing simulation.

LN. The length of the last segment LN should not exceed LNMAX (see previous). If you define too large a value of LN, the model automatically sets LN to LNMAX and issues a warning. LN also should not be less than (W+WB)/2. If you define too small a value of LN the model automatically sets LN to (W+WB)/2 and issues a warning.

AB. Angle AB (degrees) defines the direction of the bridge departure from the end of the last segment. Only 0, 90, 180 and 270 are allowed. A zero angle has a bridge that is parallel to L1 and goes to the opposite direction. Angle is measured counterclockwise. Any intermediate value of AB is set to the closest acceptable value.

MRINDSBC does not allow the bridge to overlap the last segment. If this occurs, the model changes AB so that the bridge departs in the opposite direction (this is made for correct evaluation of the capacitance coupling between bridge and inductor segments).

MRINDSBC does not allow the bridge to cross the first segment (the length of which is controlled by parameter L1) due to parasitic coupling between input and output and possible issues with layout. If MRINSB3 discovers this intersection, it displays an error and a message recommending review of the inductor layout.

BrMode. This switch defines the position of the bridge connected to port 2 relative to the inductor metal (see "Topology"). The Overpass value makes the model imply that the bridge runs above the inductor windings and is separated from the inductor metal by deposited dielectric or air. The Underpass value implies that the bridge runs atop the substrate while the inductor windings form arcs above the bridge; thus, the bridge actually runs under windings and makes the underpass (GaAs specific).

Acc. The accuracy parameter. The default value for Acc is 1. If Acc is less than 1 or greater than 10 it is set automatically to 1.

Out90deg. (layout cell parameter only): Note that the layout cell for this model has a Out90deg parameter (to edit values of this parameter select the corresponding layout cell, right-click and choose Shape Properties). On the Parameters tab of the dialog box that displays, setting this parameter to a nonzero value means that the orientation of a face at port 2 provides a connection to an external circuit via right (90deg) bend. Correspondingly, setting this parameter to zero means that the orientation of a face at port 2 provides an "in line" (no bend) connection to an external circuit. The default value is zero. Setting this to a nonzero value (for example, to 1) does not affect the electrical properties of the model; no bend component is added automatically. You can attach any bend model to the port 2 if needed.

MSUBC cover related parameters: Cover, HC, ErC, TandC, SW. Parameter Cover gives user an opportunity to chose between options "No cover" (default),""Metallic cover', and "Metallic box". Option "No cover" makes MRINDSBC to behave like MRINDSB3; Option "Metallic cover" places PEC grounded infinite plane at the elevation HC above the substrate; Option "Metallic box" confines inductor into the enclosure with PEC walls. The top PEC wall is at the height HC above the substrate, the bottom wall is represented by the grounded side of a substrate, and the side walls are at a distance SW from each side of inductor. Material parameters ErC and TandC are permittivity and loss tangent of dielectric filling under the cover.

Parameter Restrictions and Recommendations

  1. NS should be greater than 4 and less than NSMAX. The value of NSMAX can be evaluated from the condition LNMAX >0 (see previous section).

  2. The Acc parameter is limited to 1≤ACC≤10. Larger values of Acc increase the density of the mesh used in computations. The accuracy of model parameters may improve slightly from increasing Acc, at the expense of a noticeable increase in computation time. Generally, a good trade-off between accuracy and computation time is to set Acc to 1.

  3. Minimal allowed value of parameter HC (elevation of metallic cover above substrate) is limited by parameters T (thickness of winding conductor metal), TB (thickness of bridge conductor metal), and HB (thickness of bridge dielectric layer). The following limitation is imposed by common sense (cover should not touch neither inductor winding nor the strip bridge) and by the specifics of EM quasi-static technique used for modeling:

    HC > 1.053*T+HB+TB

Implementation Details

To decrease the calculation time for schematics that contain several MRINDSBC inductors, cache is implemented for this model. This means that during the first evaluation of a schematic the most time-consuming intermediate parameters for each inductor instance are being stored in a disk cache. Each inductor model checks this cache looking for its duplicate. Duplicate inductors copy the appropriate parameters from the disk cache, saving substantially on their recalculation.

Note that the model caches only frequency-independent characteristics of coupled lines, but recalculates the large equivalent circuit network (derived from coupled line characteristics) at each swept frequency. Thus, if the number of swept frequency points is large (for example, 300) the total time spent on equivalent circuit evaluation may substantially exceed the time for evaluation of coupled line characteristics. In this case, time saving due to caching may be relatively moderate.

NOTE: The implementation of EM Quasi-Static models relies heavily on the involved numerical algorithms. This may lead to a noticeable increase in simulation time for schematics that employ many such models.


This element uses line types to determine its layout. By default, the layout uses the first line type defined in your Layout Process File (LPF). You can change the element to use any of the line types configured in your process:

  1. Select the item in the layout.

  2. Right-click and choose Shape Properties to display the Cell Options dialog box.

  3. Click the Layout tab and select a Line Type.

  4. Click OK to use the new line type in the layout.

See “Cell Options Dialog Box: Layout Tab ” for Cell Options dialog box Layout tab details.

See “The Layout Process File (LPF)” for more information on editing Layout Process Files (LPFs) and to learn about adding or editing line types.


[1] M. B. Bazdar, A. R. Djordjevic, R. F. Harrington, and T. K. Sarkar, "Evaluation of quasi-static matrix parameters for multi-conductor transmission lines using Galerkin's method", IEEE Trans. Microwave Theory Tech., vol. MTT-42, July 1994, pp. 1223-1228

[2] M. Kirschning, R.H. Jansen, N.H.L. Koster, "Measurement and computer-aided modeling of microstrip discontinuities by an improved resonator method", IEEE MTT-S International Microwave Symposium Digest, 1983, pp. 495-497.

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